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You are not logged in. #1 20130208 04:20:24
Help understanding thisWhile reading about calculating the perimeter of an ellipse on the Math Is Fun website I came across a formula that I just dont understand. I am sorry that I cant seem to upload an image of the formula but its titled Infinite Series 2 and the author quotes it as being their favourite method. Thing is I dont understand how the thing breaks down in laymans terms. It has Binomial Coefficients and Factorials of Half Integers which I dont follow. Infact when I try to use my calculator to work out half integer factorials it doesnt work! I dont understand how you arrive at the numbers that you plug into this equation to obtain the answer. Because of the ruling that only established members can post links I cant show you a link to the page but it is on the Math Is Fun site. Last edited by Norvegicusbass (20130208 04:21:59) #2 20130208 04:43:11
Re: Help understanding thishi Norvegicusbass You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #3 20130208 04:49:50
Re: Help understanding thisHi The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #4 20130208 05:02:14
Re: Help understanding thisI've never seen those formulae on that page, but they do look quite interesting. Fractional factorials can be more readily computed using the gamma function, defined as: with . As for the calculation of the perimeter of an ellipse... well, my first thought was just to say General form of an ellipse: Clearly, but the arc length of a function is given by and we get here I use the substitution x = asinθ and end up with which doesn't seem to help at all and looks like I've just written the ellipse in parametric form! And I am stuck here... can anyone help? (Is this where the famed 'elliptic integrals' come from...?) #5 20130208 05:07:40
Re: Help understanding thisYou can get the perimeter of a circle easily in that integral setting a = b = 1, but for differing a and b, I am stuck. #6 20130208 05:13:15
Re: Help understanding thisHi zf. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #7 20130208 05:17:59
Re: Help understanding this
Thanks for confirmation! I just entered some random values for a and b in for WolframAlpha and it came up with that too... #8 20130208 05:22:53
Re: Help understanding thisIt's too bad that there is no exact closed formula for the ellipse circumference... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #9 20130208 20:08:31
Re: Help understanding thisThank you all for your replies. but can anyone show me how the numbers get put into this equation? I often need to see a worked example to get the feel for how these formulas work otherwise they leave me a little confused ( I am not a mathematician LOL ). I mean on that site it shows you the expansion as #10 20130208 20:15:01
Re: Help understanding thisHi Norvegicusbass using Wolfram Alpha (link). Last edited by MathsIsFun (20130211 17:27:58) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #11 20130211 10:55:16
Re: Help understanding thisYeah but even this makes little sense to me. Imagine a person you needed to explain in kindergarden language a particular mathematical term to. That person is me. Take it as a personal challenge to explain to someone dumb as me and you will cover yourself in the glory of what it is to be a true educator #12 20130211 22:23:31
Re: Help understanding this
To answer that we would have to take a look at how the formula is derived. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 